Overlap Area Computation - geospatialworldforum.org Redd… · The following are some applications...
Transcript of Overlap Area Computation - geospatialworldforum.org Redd… · The following are some applications...
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www.geospatialworldforum.org
#GWF2020
7-9 April 2020 /// Amsterdam
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Remote Sensing Applications
Images acquired from different satellites of same ground
coverage have different foot prints
Map overlay processing in Geographic Information System (GIS)
Computing an overlay of two vector maps to determine which
pairs of segments intersect.
Computer Vision
computing a partial 3D model of an environment from thousands
of partially overlapping photographs.
A casual photographer
turning overlapping photos into a single seamlessly stitched
panorama.
techniques for automatically discovering which images actually
form overlapping panoramas.
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The following are some applications where overlap
area computation is most required in satellite
imagery
• GCPs and tie point identification in common regions.
• To select best pair of images from a database of images
in the given ROI.
• Mosaicking.
• DEM evaluation in the overlap region.
• Matching of images.
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Overlap area computation between two images
Methods that use Image data
Spatial correlation
Matching technique
Methods based on geometrical aspects of foot prints
Analytical methods(integration)
Polygonal approximation
Domain Discretization Methods (Grid/Mesh)
Randomized Algorithms (Monte Carlo /Las Vegas)
When the foot prints have irregularly shaped boundary ?
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Overlay of the foot prints of non Agile and Agile satellite images
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17.45
78.4 78.45 78.5 78.55 78.617.1
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17.35
Longitude
Lat
itud
e data1data2data3data4data5data6data7data8data9
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or a combination of both…
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In both the cases the overlap is between two regularly
shaped polygons with 4 sides.
Hence the overlap area is also a polygon.
It is now sufficient to find area of a polygon.
intersection of two polygons with 4 sides
common area between A
and B with points P1, A2,
P2, B0, with c as centroid of
common region.
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Once the intersecting points are calculated, the required
area is the area inscribed in the polygon.
Area of a polygon with n sides,
say, (x1,y1), (x2,y2), …. (xn, yn)
is given by
17.4
17.45
17.5
Lat
itud
e (d
eg)
is given by
( )∑n
1i 1)n,imod(1)n,imod(
ii
yx
yxabs
2
1
= ++
78.4 78.45 78.5 78.55 78.6
17.2
17.25
17.3
17.35
Lontitude (deg)
Lat
itud
e (d
eg)
intersection points between A and B
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Monte Carlo method to find overlap area between two 4-gons.
This method uses the random numbers uniformly spread out in A and
then searches for the points of A that are also in B.
The ratio of number of common points to the total points simulated in
region A multiplied by the area of A gives the common area.
R = [x , x ] × [y , y ]
Xmin Xmax
Ymax
Ymin
R = [xmin, xmax] × [ymin, ymax]
P(x∈A ∩ B) = P(x∈R) • P(x∈A|R) • P(x∈B|A∩R)
P(A ∩ B) = P(A) •P(B|A)
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The conditional probability relationships between the initially sampled
rectangle region R = [xmin, xmax] × [ymin, ymax] and the area occupied by A in
this rectangle and then followed by area occupied by B in A are given in
sequence as P(x∈A ∩ B) = P(x∈R) • P(x∈A|R) • P(x∈B|A∩R) or simply P(A ∩ B)
= P(A) •P(B|A) since x is sampled from R.
where area(R) = ( ymax - ymin ) × ( xmax - xmin ).
The relative percentage of overlap between A and B is given by
area(B)*100/area(A).
This method is also very useful for finding areas of concave polygon regions by
suitably dividing them into appropriate convex sub regions.
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17.4
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Lat
itud
e (d
eg)
An example of Overlap area calculation for carto-2 imagery.
78.4 78.45 78.5 78.55 78.617.2
17.25
17.3
17.35
Longitude (deg)
Lat
itud
e (d
eg)
Figure: common points between A and B
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In satellite imagery, irregularly shaped
boundaries/footprints are due to the following reasons
� Camera viewing geometry
� Curvature of the ground � Curvature of the ground
� Coverage of long passes
� Imaging over Polar regions
� Projection of the imaged area on to a plane.
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A shape of double concave outline is shown in figure (1a),
and a sheared form of it is shown in figure (1b).
A case arises when imaging over the polar regions, if the spacecraft also
possesses roll movement then the corresponding imaged shape file
resembles like half the negative meniscus lens as shown in figure (1c),
High oblique images looks like figure (1d).
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Few examples images acquired from TMC of Chandrayaan-1
Near Polar region
Nadir, Aft, Fore (Orbit No. 2488) Nadir, Aft (Orbit No. 2432)
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Overlap area calculation
Analytical Method
Border coordinates are given in terms of latitudes and longitudes, say, (xi,yi)
Assuming that the closed shape bounded by four curves is approximated by
four polynomials of degree n of the form
where i = 1, 2, 3, 4. -----(1)
Perform a polynomial curve fit to the bounding curves of the footprint.
0
2n
2n
1n
1n
nn
ni a...αaαaαa)α(P ++++=
Perform a polynomial curve fit to the bounding curves of the footprint.
A D
P4 P2
EB CF
X=x2X=x1
P1
P
P3
••••
•••• ••••
••••
X
Y
Y=y2
Y=y1
∫∫P
dydxArea =
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The overlap area enclosed in
the Region bounded by
two straight lines
Practically, two sides of the closed shape are bounded
by straight line as they correspond to the camera start
and end scan lines.
two straight lines
(y=y1, y=y2),
and two polynomials
( x=Q1(y), x=Q2(y) ),
given by
∫ ∫2
1
2
1
y
yy
)y(Q
)y(Qx
dydxArea= =
=
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Different Cases of overlap region
Complexity increases with more number of intersecting points
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Monte Carlo method to find overlap area between two shapes
This method uses the random numbers uniformly spread out in A and then
searches for the points of A that are also in B ( see figure ).
The ratio of number of common points to the total points simulated in
region A multiplied by the area of A gives the common area
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80
85
90
Lo
ng
itud
e(d
eg)
ForeNadir
A case of TMC image of Chandrayaan-1, orbit No. 2522.
10 20 30 40 50 60 70
65
70
75
Latitude(deg)
Lo
ng
itud
e(d
eg)
NadirAft
Coverage of Nadir, Fore and Aft foot
prints of TMC image (orbit no. 2522)
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40
45
50
55
Lat
itud
e(d
eg)
DataPolynomial Approx
35
40
45
50
55
60
65
Lat
itud
e(d
eg)
DataPolynomial Approx
Polynomial approximation of foot print boundaries
65 70 75 80 8530
35
Longitude (deg)
70 75 80 85 90
20
25
30
35
Longitude(deg)
Fore image foot print and its polynomial
approximation.
Nadir image foot print and its
polynomial approximation.
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40
45
50
55
60
65
65 70 75 80 85 9020
25
30
35
the overlap area calculation between Nadir
and Fore shape files for N=5000 simulations.
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